Abstract

We propose and design a germanium (Ge) waveguide laser under external phonon injection to reduce laser threshold. To take the phonon injection and the acousto-optic overlap into consideration, the theory of the photon-phonon laser action is further developed. The phononic crystal waveguide is introduced in the laser structure to intensify acousto-optic interaction, and characteristics of photon-phonon laser action in Ge waveguide are analyzed. With the external phonon injection, the two-quantum transition can be facilitated and the photon-phonon laser action is able to be established. The impacts of phononic crystal waveguide parameters, overlap of optical and acoustic fields, and phonon injection on the laser behavior are discussed. Optimal waveguide structural parameters are obtained to enhance acousto-optic interaction through the enlargement of the overlap of optical and acoustic fields. The results indicate that, for a Ge waveguide with the length of 200 μm, the threshold current is reduced to 0.2 μA and the slope efficiency reaches 0.7 W/A when the average phonon injection concentration is about 2.5 × 1021 cm−3. Our proposed scheme offers an effective approach to achieve laser oscillation in integrated Ge waveguide.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Ultrafast excitation of conduction-band electrons by high-intensity ultrashort laser pulses in band-gap solids: Vinogradov equation versus Drude model

Olga Sergaeva, Vitaly Gruzdev, Drake Austin, and Enam Chowdhury
J. Opt. Soc. Am. B 35(11) 2895-2905 (2018)

Intensity noise properties of quantum cascade lasers

Tobias Gensty, Wolfgang Elsäßer, and Christian Mann
Opt. Express 13(6) 2032-2039 (2005)

References

  • View by:
  • |
  • |
  • |

  1. Y. Vlasov and S. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12(8), 1622–1631 (2004).
    [Crossref] [PubMed]
  2. G. Z. Mashanovich, M. M. Milošević, M. Nedeljkovic, N. Owens, B. Xiong, E. J. Teo, and Y. Hu, “Low loss silicon waveguides for the mid-infrared,” Opt. Express 19(8), 7112–7119 (2011).
    [Crossref] [PubMed]
  3. T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87(15), 151112 (2005).
    [Crossref]
  4. G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
    [Crossref]
  5. D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s Silicon Optical Modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
    [Crossref]
  6. L. Vivien, J. Osmond, J. M. Fédéli, D. Marris-Morini, P. Crozat, J. F. Damlencourt, E. Cassan, Y. Lecunff, and S. Laval, “42 GHz p.i.n Germanium photodetector integrated in a silicon-on-insulator waveguide,” Opt. Express 17(8), 6252–6257 (2009).
    [Crossref] [PubMed]
  7. J. Michel, J. Liu, and L. C. Kimerling, “High-performance Ge-on-Si photodetectors,” Nat. Photonics 4(8), 527–534 (2010).
    [Crossref]
  8. K. Tanabe, K. Watanabe, and Y. Arakawa, “III-V/Si hybrid photonic devices by direct fusion bonding,” Sci. Rep. 2, 349 (2012).
    [Crossref] [PubMed]
  9. H. Yang, D. Zhao, S. Chuwongin, J. H. Seo, W. Yang, Y. Shuai, J. Berggren, M. Hammar, Z. Ma, and W. Zhou, “Transfer-printed stacked nanomembrane lasers on silicon,” Nat. Photonics 6(9), 615 (2012).
    [Crossref]
  10. H. Liu, T. Wang, Q. Jiang, R. Hogg, F. Tutu, F. Pozzi, and A. Seeds, “Long-wavelength InAs/GaAs quantum-dot laser diode monolithically grown on Ge substrate,” Nat. Photonics 5(7), 416–419 (2011).
    [Crossref]
  11. R. Koerner, M. Oehme, M. Gollhofer, M. Schmid, K. Kostecki, S. Bechler, D. Widmann, E. Kasper, and J. Schulze, “Electrically pumped lasing from Ge Fabry-Perot resonators on Si,” Opt. Express 23(11), 14815–14822 (2015).
    [Crossref] [PubMed]
  12. J. Liu, X. Sun, D. Pan, X. Wang, L. C. Kimerling, T. L. Koch, and J. Michel, “Tensile-strained, n-type Ge as a gain medium for monolithic laser integration on Si,” Opt. Express 15(18), 11272–11277 (2007).
    [Crossref] [PubMed]
  13. R. E. Camacho-Aguilera, Y. Cai, N. Patel, J. T. Bessette, M. Romagnoli, L. C. Kimerling, and J. Michel, “An electrically pumped germanium laser,” Opt. Express 20(10), 11316–11320 (2012).
    [Crossref] [PubMed]
  14. M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
    [Crossref]
  15. S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
    [Crossref]
  16. G. Sun, R. A. Soref, and H. H. Cheng, “Design of an electrically pumped SiGeSn/GeSn/SiGeSn double-heterostructure mid-infrared laser,” J. Appl. Phys. 108(3), 033107 (2010).
    [Crossref]
  17. G. Sun, R. A. Soref, and H. H. Cheng, “Design of a Si-based lattice-matched room-temperature GeSn/GeSiSn multi-quantum-well mid-infrared laser diode,” Opt. Express 18(19), 19957–19965 (2010).
    [Crossref] [PubMed]
  18. Z. Zhou, B. Yin, and J. Michel, “On-chip light sources for silicon photonics,” Light Sci. Appl. 4(11), e358 (2015).
    [Crossref] [PubMed]
  19. A. A. Zadernovskiĭ and L. A. Rivlin, “Stimulated two-quantum photon–phonon transitions in indirect-gap semiconductors,” Sov. J. Quantum Electron. 21(3), 255–260 (1991).
    [Crossref]
  20. A. A. Zadernovskiĭ and L. A. Rivlin, “Photon-phonon laser action in indirect-gap semiconductors,” Quantum Electron. 23(4), 300–308 (1993).
    [Crossref]
  21. R. Zhang and J. Sun, “Design of Silicon Phoxonic Crystal Waveguides for Slow Light Enhanced Forward Stimulated Brillouin Scattering,” J. Lightwave Technol. 35(14), 2917–2925 (2017).
    [Crossref]
  22. F. Hsu, C. Lee, J. Hsu, T. Huang, C. Wang, and P. Chang, “Acoustic band gaps in phononic crystal strip waveguides,” Appl. Phys. Lett. 96(5), 051902 (2010).
    [Crossref]
  23. J. M. Escalante, A. Martínez, and V. Laude, “Design of single-mode waveguides for enhanced light-sound interaction in honeycomb-lattice silicon slabs,” J. Appl. Phys. 115(6), 064302 (2014).
    [Crossref]
  24. S. Gevorgian, A. Tagantsev, and A. K. Vorobiev, Tuneable film bulk acoustic wave resonators (Springer Science & Business Media, 2013).
  25. G. Chen, R. Zhang, J. Sun, H. Xie, Y. Gao, D. Feng, and H. Xiong, “Mode conversion based on forward stimulated Brillouin scattering in a hybrid phononic-photonic waveguide,” Opt. Express 22(26), 32060–32070 (2014).
    [Crossref] [PubMed]
  26. G. Chen, R. Zhang, and J. Sun, “On-chip optical mode conversion based on dynamic grating in photonic-phononic hybrid waveguide,” Sci. Rep. 5(1), 10346 (2015).
    [Crossref] [PubMed]
  27. V. Laude, J. C. Beugnot, S. Benchabane, Y. Pennec, B. Djafari-Rouhani, N. Papanikolaou, J. M. Escalante, and A. Martinez, “Simultaneous guidance of slow photons and slow acoustic phonons in silicon phoxonic crystal slabs,” Opt. Express 19(10), 9690–9698 (2011).
    [Crossref] [PubMed]
  28. A. Ciesielski, L. Skowronski, W. Pacuski, and T. Szoplik, “Permittivity of Ge, Te and Se thin films in the 200–1500 nm spectral range. Predicting the segregation effects in silver,” Mater. Sci. Semicond. Process. 81, 64–67 (2018).
    [Crossref]
  29. K. Luke, Y. Okawachi, M. R. E. Lamont, A. L. Gaeta, and M. Lipson, “Broadband mid-infrared frequency comb generation in a Si(3)N(4) microresonator,” Opt. Lett. 40(21), 4823–4826 (2015).
    [Crossref] [PubMed]

2018 (1)

A. Ciesielski, L. Skowronski, W. Pacuski, and T. Szoplik, “Permittivity of Ge, Te and Se thin films in the 200–1500 nm spectral range. Predicting the segregation effects in silver,” Mater. Sci. Semicond. Process. 81, 64–67 (2018).
[Crossref]

2017 (1)

2015 (5)

G. Chen, R. Zhang, and J. Sun, “On-chip optical mode conversion based on dynamic grating in photonic-phononic hybrid waveguide,” Sci. Rep. 5(1), 10346 (2015).
[Crossref] [PubMed]

K. Luke, Y. Okawachi, M. R. E. Lamont, A. L. Gaeta, and M. Lipson, “Broadband mid-infrared frequency comb generation in a Si(3)N(4) microresonator,” Opt. Lett. 40(21), 4823–4826 (2015).
[Crossref] [PubMed]

R. Koerner, M. Oehme, M. Gollhofer, M. Schmid, K. Kostecki, S. Bechler, D. Widmann, E. Kasper, and J. Schulze, “Electrically pumped lasing from Ge Fabry-Perot resonators on Si,” Opt. Express 23(11), 14815–14822 (2015).
[Crossref] [PubMed]

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

Z. Zhou, B. Yin, and J. Michel, “On-chip light sources for silicon photonics,” Light Sci. Appl. 4(11), e358 (2015).
[Crossref] [PubMed]

2014 (2)

J. M. Escalante, A. Martínez, and V. Laude, “Design of single-mode waveguides for enhanced light-sound interaction in honeycomb-lattice silicon slabs,” J. Appl. Phys. 115(6), 064302 (2014).
[Crossref]

G. Chen, R. Zhang, J. Sun, H. Xie, Y. Gao, D. Feng, and H. Xiong, “Mode conversion based on forward stimulated Brillouin scattering in a hybrid phononic-photonic waveguide,” Opt. Express 22(26), 32060–32070 (2014).
[Crossref] [PubMed]

2013 (1)

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

2012 (4)

R. E. Camacho-Aguilera, Y. Cai, N. Patel, J. T. Bessette, M. Romagnoli, L. C. Kimerling, and J. Michel, “An electrically pumped germanium laser,” Opt. Express 20(10), 11316–11320 (2012).
[Crossref] [PubMed]

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s Silicon Optical Modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

K. Tanabe, K. Watanabe, and Y. Arakawa, “III-V/Si hybrid photonic devices by direct fusion bonding,” Sci. Rep. 2, 349 (2012).
[Crossref] [PubMed]

H. Yang, D. Zhao, S. Chuwongin, J. H. Seo, W. Yang, Y. Shuai, J. Berggren, M. Hammar, Z. Ma, and W. Zhou, “Transfer-printed stacked nanomembrane lasers on silicon,” Nat. Photonics 6(9), 615 (2012).
[Crossref]

2011 (3)

2010 (5)

F. Hsu, C. Lee, J. Hsu, T. Huang, C. Wang, and P. Chang, “Acoustic band gaps in phononic crystal strip waveguides,” Appl. Phys. Lett. 96(5), 051902 (2010).
[Crossref]

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

J. Michel, J. Liu, and L. C. Kimerling, “High-performance Ge-on-Si photodetectors,” Nat. Photonics 4(8), 527–534 (2010).
[Crossref]

G. Sun, R. A. Soref, and H. H. Cheng, “Design of an electrically pumped SiGeSn/GeSn/SiGeSn double-heterostructure mid-infrared laser,” J. Appl. Phys. 108(3), 033107 (2010).
[Crossref]

G. Sun, R. A. Soref, and H. H. Cheng, “Design of a Si-based lattice-matched room-temperature GeSn/GeSiSn multi-quantum-well mid-infrared laser diode,” Opt. Express 18(19), 19957–19965 (2010).
[Crossref] [PubMed]

2009 (1)

2007 (1)

2005 (1)

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87(15), 151112 (2005).
[Crossref]

2004 (1)

1993 (1)

A. A. Zadernovskiĭ and L. A. Rivlin, “Photon-phonon laser action in indirect-gap semiconductors,” Quantum Electron. 23(4), 300–308 (1993).
[Crossref]

1991 (1)

A. A. Zadernovskiĭ and L. A. Rivlin, “Stimulated two-quantum photon–phonon transitions in indirect-gap semiconductors,” Sov. J. Quantum Electron. 21(3), 255–260 (1991).
[Crossref]

Alic, N.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s Silicon Optical Modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

Arakawa, Y.

K. Tanabe, K. Watanabe, and Y. Arakawa, “III-V/Si hybrid photonic devices by direct fusion bonding,” Sci. Rep. 2, 349 (2012).
[Crossref] [PubMed]

Bechler, S.

Benchabane, S.

Berggren, J.

H. Yang, D. Zhao, S. Chuwongin, J. H. Seo, W. Yang, Y. Shuai, J. Berggren, M. Hammar, Z. Ma, and W. Zhou, “Transfer-printed stacked nanomembrane lasers on silicon,” Nat. Photonics 6(9), 615 (2012).
[Crossref]

Bessette, J. T.

Beugnot, J. C.

Buca, D.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

Cai, Y.

Camacho-Aguilera, R. E.

Cassan, E.

Chang, P.

F. Hsu, C. Lee, J. Hsu, T. Huang, C. Wang, and P. Chang, “Acoustic band gaps in phononic crystal strip waveguides,” Appl. Phys. Lett. 96(5), 051902 (2010).
[Crossref]

Chen, G.

Cheng, H. H.

G. Sun, R. A. Soref, and H. H. Cheng, “Design of a Si-based lattice-matched room-temperature GeSn/GeSiSn multi-quantum-well mid-infrared laser diode,” Opt. Express 18(19), 19957–19965 (2010).
[Crossref] [PubMed]

G. Sun, R. A. Soref, and H. H. Cheng, “Design of an electrically pumped SiGeSn/GeSn/SiGeSn double-heterostructure mid-infrared laser,” J. Appl. Phys. 108(3), 033107 (2010).
[Crossref]

Chiussi, S.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

Chrastina, D.

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

Chuwongin, S.

H. Yang, D. Zhao, S. Chuwongin, J. H. Seo, W. Yang, Y. Shuai, J. Berggren, M. Hammar, Z. Ma, and W. Zhou, “Transfer-printed stacked nanomembrane lasers on silicon,” Nat. Photonics 6(9), 615 (2012).
[Crossref]

Ciesielski, A.

A. Ciesielski, L. Skowronski, W. Pacuski, and T. Szoplik, “Permittivity of Ge, Te and Se thin films in the 200–1500 nm spectral range. Predicting the segregation effects in silver,” Mater. Sci. Semicond. Process. 81, 64–67 (2018).
[Crossref]

Crozat, P.

Damlencourt, J. F.

Djafari-Rouhani, B.

Escalante, J. M.

Faist, J.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

Fedeli, J.-M.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s Silicon Optical Modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

Fédéli, J. M.

Feng, D.

Frigerio, J.

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

Gaeta, A. L.

Gao, Y.

Gardes, F. Y.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s Silicon Optical Modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Geiger, R.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

Gollhofer, M.

Grützmacher, D.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

Hammar, M.

H. Yang, D. Zhao, S. Chuwongin, J. H. Seo, W. Yang, Y. Shuai, J. Berggren, M. Hammar, Z. Ma, and W. Zhou, “Transfer-printed stacked nanomembrane lasers on silicon,” Nat. Photonics 6(9), 615 (2012).
[Crossref]

Hartmann, J. M.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

Hogg, R.

H. Liu, T. Wang, Q. Jiang, R. Hogg, F. Tutu, F. Pozzi, and A. Seeds, “Long-wavelength InAs/GaAs quantum-dot laser diode monolithically grown on Ge substrate,” Nat. Photonics 5(7), 416–419 (2011).
[Crossref]

Hsu, F.

F. Hsu, C. Lee, J. Hsu, T. Huang, C. Wang, and P. Chang, “Acoustic band gaps in phononic crystal strip waveguides,” Appl. Phys. Lett. 96(5), 051902 (2010).
[Crossref]

Hsu, J.

F. Hsu, C. Lee, J. Hsu, T. Huang, C. Wang, and P. Chang, “Acoustic band gaps in phononic crystal strip waveguides,” Appl. Phys. Lett. 96(5), 051902 (2010).
[Crossref]

Hu, Y.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s Silicon Optical Modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

G. Z. Mashanovich, M. M. Milošević, M. Nedeljkovic, N. Owens, B. Xiong, E. J. Teo, and Y. Hu, “Low loss silicon waveguides for the mid-infrared,” Opt. Express 19(8), 7112–7119 (2011).
[Crossref] [PubMed]

Huang, T.

F. Hsu, C. Lee, J. Hsu, T. Huang, C. Wang, and P. Chang, “Acoustic band gaps in phononic crystal strip waveguides,” Appl. Phys. Lett. 96(5), 051902 (2010).
[Crossref]

Ikonic, Z.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

Isella, G.

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

Jiang, Q.

H. Liu, T. Wang, Q. Jiang, R. Hogg, F. Tutu, F. Pozzi, and A. Seeds, “Long-wavelength InAs/GaAs quantum-dot laser diode monolithically grown on Ge substrate,” Nat. Photonics 5(7), 416–419 (2011).
[Crossref]

Kasper, E.

Kimerling, L. C.

Koch, T. L.

Koerner, R.

Kostecki, K.

Kuo, B. P. P.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s Silicon Optical Modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

Kuramochi, E.

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87(15), 151112 (2005).
[Crossref]

Lamont, M. R. E.

Laude, V.

Laval, S.

Lecunff, Y.

Lee, C.

F. Hsu, C. Lee, J. Hsu, T. Huang, C. Wang, and P. Chang, “Acoustic band gaps in phononic crystal strip waveguides,” Appl. Phys. Lett. 96(5), 051902 (2010).
[Crossref]

Lipson, M.

Liu, H.

H. Liu, T. Wang, Q. Jiang, R. Hogg, F. Tutu, F. Pozzi, and A. Seeds, “Long-wavelength InAs/GaAs quantum-dot laser diode monolithically grown on Ge substrate,” Nat. Photonics 5(7), 416–419 (2011).
[Crossref]

Liu, J.

Luke, K.

Luysberg, M.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

Ma, Z.

H. Yang, D. Zhao, S. Chuwongin, J. H. Seo, W. Yang, Y. Shuai, J. Berggren, M. Hammar, Z. Ma, and W. Zhou, “Transfer-printed stacked nanomembrane lasers on silicon,” Nat. Photonics 6(9), 615 (2012).
[Crossref]

Mantl, S.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

Marris-Morini, D.

Martinez, A.

Martínez, A.

J. M. Escalante, A. Martínez, and V. Laude, “Design of single-mode waveguides for enhanced light-sound interaction in honeycomb-lattice silicon slabs,” J. Appl. Phys. 115(6), 064302 (2014).
[Crossref]

Mashanovich, G.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Mashanovich, G. Z.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s Silicon Optical Modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

G. Z. Mashanovich, M. M. Milošević, M. Nedeljkovic, N. Owens, B. Xiong, E. J. Teo, and Y. Hu, “Low loss silicon waveguides for the mid-infrared,” Opt. Express 19(8), 7112–7119 (2011).
[Crossref] [PubMed]

McNab, S.

Michel, J.

Miloševic, M. M.

Minamisawa, R. A.

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

Mitsugi, S.

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87(15), 151112 (2005).
[Crossref]

Mussler, G.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

Myslivets, E.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s Silicon Optical Modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

Nedeljkovic, M.

Notomi, M.

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87(15), 151112 (2005).
[Crossref]

Oehme, M.

Okawachi, Y.

Osmond, J.

Owens, N.

Pacuski, W.

A. Ciesielski, L. Skowronski, W. Pacuski, and T. Szoplik, “Permittivity of Ge, Te and Se thin films in the 200–1500 nm spectral range. Predicting the segregation effects in silver,” Mater. Sci. Semicond. Process. 81, 64–67 (2018).
[Crossref]

Pan, D.

Papanikolaou, N.

Patel, N.

Pennec, Y.

Pozzi, F.

H. Liu, T. Wang, Q. Jiang, R. Hogg, F. Tutu, F. Pozzi, and A. Seeds, “Long-wavelength InAs/GaAs quantum-dot laser diode monolithically grown on Ge substrate,” Nat. Photonics 5(7), 416–419 (2011).
[Crossref]

Radic, S.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s Silicon Optical Modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

Reed, G. T.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s Silicon Optical Modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Rivlin, L. A.

A. A. Zadernovskiĭ and L. A. Rivlin, “Photon-phonon laser action in indirect-gap semiconductors,” Quantum Electron. 23(4), 300–308 (1993).
[Crossref]

A. A. Zadernovskiĭ and L. A. Rivlin, “Stimulated two-quantum photon–phonon transitions in indirect-gap semiconductors,” Sov. J. Quantum Electron. 21(3), 255–260 (1991).
[Crossref]

Romagnoli, M.

Schiefler, G.

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

Schmid, M.

Schulze, J.

Seeds, A.

H. Liu, T. Wang, Q. Jiang, R. Hogg, F. Tutu, F. Pozzi, and A. Seeds, “Long-wavelength InAs/GaAs quantum-dot laser diode monolithically grown on Ge substrate,” Nat. Photonics 5(7), 416–419 (2011).
[Crossref]

Seo, J. H.

H. Yang, D. Zhao, S. Chuwongin, J. H. Seo, W. Yang, Y. Shuai, J. Berggren, M. Hammar, Z. Ma, and W. Zhou, “Transfer-printed stacked nanomembrane lasers on silicon,” Nat. Photonics 6(9), 615 (2012).
[Crossref]

Shinya, A.

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87(15), 151112 (2005).
[Crossref]

Shuai, Y.

H. Yang, D. Zhao, S. Chuwongin, J. H. Seo, W. Yang, Y. Shuai, J. Berggren, M. Hammar, Z. Ma, and W. Zhou, “Transfer-printed stacked nanomembrane lasers on silicon,” Nat. Photonics 6(9), 615 (2012).
[Crossref]

Sigg, H.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

Skowronski, L.

A. Ciesielski, L. Skowronski, W. Pacuski, and T. Szoplik, “Permittivity of Ge, Te and Se thin films in the 200–1500 nm spectral range. Predicting the segregation effects in silver,” Mater. Sci. Semicond. Process. 81, 64–67 (2018).
[Crossref]

Soref, R. A.

G. Sun, R. A. Soref, and H. H. Cheng, “Design of a Si-based lattice-matched room-temperature GeSn/GeSiSn multi-quantum-well mid-infrared laser diode,” Opt. Express 18(19), 19957–19965 (2010).
[Crossref] [PubMed]

G. Sun, R. A. Soref, and H. H. Cheng, “Design of an electrically pumped SiGeSn/GeSn/SiGeSn double-heterostructure mid-infrared laser,” J. Appl. Phys. 108(3), 033107 (2010).
[Crossref]

Spolenak, R.

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

Stoica, T.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

Süess, M. J.

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

Sun, G.

G. Sun, R. A. Soref, and H. H. Cheng, “Design of an electrically pumped SiGeSn/GeSn/SiGeSn double-heterostructure mid-infrared laser,” J. Appl. Phys. 108(3), 033107 (2010).
[Crossref]

G. Sun, R. A. Soref, and H. H. Cheng, “Design of a Si-based lattice-matched room-temperature GeSn/GeSiSn multi-quantum-well mid-infrared laser diode,” Opt. Express 18(19), 19957–19965 (2010).
[Crossref] [PubMed]

Sun, J.

Sun, X.

Szoplik, T.

A. Ciesielski, L. Skowronski, W. Pacuski, and T. Szoplik, “Permittivity of Ge, Te and Se thin films in the 200–1500 nm spectral range. Predicting the segregation effects in silver,” Mater. Sci. Semicond. Process. 81, 64–67 (2018).
[Crossref]

Tanabe, K.

K. Tanabe, K. Watanabe, and Y. Arakawa, “III-V/Si hybrid photonic devices by direct fusion bonding,” Sci. Rep. 2, 349 (2012).
[Crossref] [PubMed]

Tanabe, T.

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87(15), 151112 (2005).
[Crossref]

Teo, E. J.

Thomson, D. J.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s Silicon Optical Modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Tutu, F.

H. Liu, T. Wang, Q. Jiang, R. Hogg, F. Tutu, F. Pozzi, and A. Seeds, “Long-wavelength InAs/GaAs quantum-dot laser diode monolithically grown on Ge substrate,” Nat. Photonics 5(7), 416–419 (2011).
[Crossref]

Vivien, L.

Vlasov, Y.

von den Driesch, N.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

Wang, C.

F. Hsu, C. Lee, J. Hsu, T. Huang, C. Wang, and P. Chang, “Acoustic band gaps in phononic crystal strip waveguides,” Appl. Phys. Lett. 96(5), 051902 (2010).
[Crossref]

Wang, T.

H. Liu, T. Wang, Q. Jiang, R. Hogg, F. Tutu, F. Pozzi, and A. Seeds, “Long-wavelength InAs/GaAs quantum-dot laser diode monolithically grown on Ge substrate,” Nat. Photonics 5(7), 416–419 (2011).
[Crossref]

Wang, X.

Watanabe, K.

K. Tanabe, K. Watanabe, and Y. Arakawa, “III-V/Si hybrid photonic devices by direct fusion bonding,” Sci. Rep. 2, 349 (2012).
[Crossref] [PubMed]

Widmann, D.

Wirths, S.

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

Xie, H.

Xiong, B.

Xiong, H.

Yang, H.

H. Yang, D. Zhao, S. Chuwongin, J. H. Seo, W. Yang, Y. Shuai, J. Berggren, M. Hammar, Z. Ma, and W. Zhou, “Transfer-printed stacked nanomembrane lasers on silicon,” Nat. Photonics 6(9), 615 (2012).
[Crossref]

Yang, W.

H. Yang, D. Zhao, S. Chuwongin, J. H. Seo, W. Yang, Y. Shuai, J. Berggren, M. Hammar, Z. Ma, and W. Zhou, “Transfer-printed stacked nanomembrane lasers on silicon,” Nat. Photonics 6(9), 615 (2012).
[Crossref]

Yin, B.

Z. Zhou, B. Yin, and J. Michel, “On-chip light sources for silicon photonics,” Light Sci. Appl. 4(11), e358 (2015).
[Crossref] [PubMed]

Zadernovskii, A. A.

A. A. Zadernovskiĭ and L. A. Rivlin, “Photon-phonon laser action in indirect-gap semiconductors,” Quantum Electron. 23(4), 300–308 (1993).
[Crossref]

A. A. Zadernovskiĭ and L. A. Rivlin, “Stimulated two-quantum photon–phonon transitions in indirect-gap semiconductors,” Sov. J. Quantum Electron. 21(3), 255–260 (1991).
[Crossref]

Zhang, R.

Zhao, D.

H. Yang, D. Zhao, S. Chuwongin, J. H. Seo, W. Yang, Y. Shuai, J. Berggren, M. Hammar, Z. Ma, and W. Zhou, “Transfer-printed stacked nanomembrane lasers on silicon,” Nat. Photonics 6(9), 615 (2012).
[Crossref]

Zhou, W.

H. Yang, D. Zhao, S. Chuwongin, J. H. Seo, W. Yang, Y. Shuai, J. Berggren, M. Hammar, Z. Ma, and W. Zhou, “Transfer-printed stacked nanomembrane lasers on silicon,” Nat. Photonics 6(9), 615 (2012).
[Crossref]

Zhou, Z.

Z. Zhou, B. Yin, and J. Michel, “On-chip light sources for silicon photonics,” Light Sci. Appl. 4(11), e358 (2015).
[Crossref] [PubMed]

Zlatanovic, S.

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s Silicon Optical Modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

Appl. Phys. Lett. (2)

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87(15), 151112 (2005).
[Crossref]

F. Hsu, C. Lee, J. Hsu, T. Huang, C. Wang, and P. Chang, “Acoustic band gaps in phononic crystal strip waveguides,” Appl. Phys. Lett. 96(5), 051902 (2010).
[Crossref]

IEEE Photonics Technol. Lett. (1)

D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s Silicon Optical Modulator,” IEEE Photonics Technol. Lett. 24(4), 234–236 (2012).
[Crossref]

J. Appl. Phys. (2)

G. Sun, R. A. Soref, and H. H. Cheng, “Design of an electrically pumped SiGeSn/GeSn/SiGeSn double-heterostructure mid-infrared laser,” J. Appl. Phys. 108(3), 033107 (2010).
[Crossref]

J. M. Escalante, A. Martínez, and V. Laude, “Design of single-mode waveguides for enhanced light-sound interaction in honeycomb-lattice silicon slabs,” J. Appl. Phys. 115(6), 064302 (2014).
[Crossref]

J. Lightwave Technol. (1)

Light Sci. Appl. (1)

Z. Zhou, B. Yin, and J. Michel, “On-chip light sources for silicon photonics,” Light Sci. Appl. 4(11), e358 (2015).
[Crossref] [PubMed]

Mater. Sci. Semicond. Process. (1)

A. Ciesielski, L. Skowronski, W. Pacuski, and T. Szoplik, “Permittivity of Ge, Te and Se thin films in the 200–1500 nm spectral range. Predicting the segregation effects in silver,” Mater. Sci. Semicond. Process. 81, 64–67 (2018).
[Crossref]

Nat. Photonics (6)

M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schiefler, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist, and H. Sigg, “Analysis of enhanced light emission from highly strained germanium microbridges,” Nat. Photonics 7(6), 466–472 (2013).
[Crossref]

S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca, and D. Grützmacher, “Lasing in direct-bandgap GeSn alloy grown on Si,” Nat. Photonics 9(2), 88–92 (2015).
[Crossref]

H. Yang, D. Zhao, S. Chuwongin, J. H. Seo, W. Yang, Y. Shuai, J. Berggren, M. Hammar, Z. Ma, and W. Zhou, “Transfer-printed stacked nanomembrane lasers on silicon,” Nat. Photonics 6(9), 615 (2012).
[Crossref]

H. Liu, T. Wang, Q. Jiang, R. Hogg, F. Tutu, F. Pozzi, and A. Seeds, “Long-wavelength InAs/GaAs quantum-dot laser diode monolithically grown on Ge substrate,” Nat. Photonics 5(7), 416–419 (2011).
[Crossref]

J. Michel, J. Liu, and L. C. Kimerling, “High-performance Ge-on-Si photodetectors,” Nat. Photonics 4(8), 527–534 (2010).
[Crossref]

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Opt. Express (9)

Y. Vlasov and S. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12(8), 1622–1631 (2004).
[Crossref] [PubMed]

G. Z. Mashanovich, M. M. Milošević, M. Nedeljkovic, N. Owens, B. Xiong, E. J. Teo, and Y. Hu, “Low loss silicon waveguides for the mid-infrared,” Opt. Express 19(8), 7112–7119 (2011).
[Crossref] [PubMed]

L. Vivien, J. Osmond, J. M. Fédéli, D. Marris-Morini, P. Crozat, J. F. Damlencourt, E. Cassan, Y. Lecunff, and S. Laval, “42 GHz p.i.n Germanium photodetector integrated in a silicon-on-insulator waveguide,” Opt. Express 17(8), 6252–6257 (2009).
[Crossref] [PubMed]

R. Koerner, M. Oehme, M. Gollhofer, M. Schmid, K. Kostecki, S. Bechler, D. Widmann, E. Kasper, and J. Schulze, “Electrically pumped lasing from Ge Fabry-Perot resonators on Si,” Opt. Express 23(11), 14815–14822 (2015).
[Crossref] [PubMed]

J. Liu, X. Sun, D. Pan, X. Wang, L. C. Kimerling, T. L. Koch, and J. Michel, “Tensile-strained, n-type Ge as a gain medium for monolithic laser integration on Si,” Opt. Express 15(18), 11272–11277 (2007).
[Crossref] [PubMed]

R. E. Camacho-Aguilera, Y. Cai, N. Patel, J. T. Bessette, M. Romagnoli, L. C. Kimerling, and J. Michel, “An electrically pumped germanium laser,” Opt. Express 20(10), 11316–11320 (2012).
[Crossref] [PubMed]

G. Sun, R. A. Soref, and H. H. Cheng, “Design of a Si-based lattice-matched room-temperature GeSn/GeSiSn multi-quantum-well mid-infrared laser diode,” Opt. Express 18(19), 19957–19965 (2010).
[Crossref] [PubMed]

V. Laude, J. C. Beugnot, S. Benchabane, Y. Pennec, B. Djafari-Rouhani, N. Papanikolaou, J. M. Escalante, and A. Martinez, “Simultaneous guidance of slow photons and slow acoustic phonons in silicon phoxonic crystal slabs,” Opt. Express 19(10), 9690–9698 (2011).
[Crossref] [PubMed]

G. Chen, R. Zhang, J. Sun, H. Xie, Y. Gao, D. Feng, and H. Xiong, “Mode conversion based on forward stimulated Brillouin scattering in a hybrid phononic-photonic waveguide,” Opt. Express 22(26), 32060–32070 (2014).
[Crossref] [PubMed]

Opt. Lett. (1)

Quantum Electron. (1)

A. A. Zadernovskiĭ and L. A. Rivlin, “Photon-phonon laser action in indirect-gap semiconductors,” Quantum Electron. 23(4), 300–308 (1993).
[Crossref]

Sci. Rep. (2)

G. Chen, R. Zhang, and J. Sun, “On-chip optical mode conversion based on dynamic grating in photonic-phononic hybrid waveguide,” Sci. Rep. 5(1), 10346 (2015).
[Crossref] [PubMed]

K. Tanabe, K. Watanabe, and Y. Arakawa, “III-V/Si hybrid photonic devices by direct fusion bonding,” Sci. Rep. 2, 349 (2012).
[Crossref] [PubMed]

Sov. J. Quantum Electron. (1)

A. A. Zadernovskiĭ and L. A. Rivlin, “Stimulated two-quantum photon–phonon transitions in indirect-gap semiconductors,” Sov. J. Quantum Electron. 21(3), 255–260 (1991).
[Crossref]

Other (1)

S. Gevorgian, A. Tagantsev, and A. K. Vorobiev, Tuneable film bulk acoustic wave resonators (Springer Science & Business Media, 2013).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (15)

Fig. 1
Fig. 1 Schematic of two-quantum transition in Ge. Electrons are pumped from the valence band to the conduction band in the rate of Wp. Both phonon and photon emissions include spontaneous processes and stimulated processes. Wkq, Wk0, W0q and W00 are transition rates. The subscripts k, q and 0 represent the photon stimulated emission, the phonon stimulated emission and spontaneous emission, respectively.
Fig. 2
Fig. 2 (a) The dimensionless average photon concentration n k ¯ as a function of the pumping rate of electrons into the conduction band ( W p ¯ / W 0 ) th with the dimensionless average phonon injection concentrations n 0 ¯ of 0, 0.5 and 1.6 when assuming V k q =1 and the optical field and acoustic field are perfectly confined. The dash lines are asymptotes of the bottoms of the solid lines. (b) Magnified view of the blue line near the origin point.
Fig. 3
Fig. 3 (a) Dependences of the threshold of the pumping rate of electrons into the conduction band ( W p ¯ / W 0 ) th on the dimensionless average phonon injection concentrations n 0 ¯ under various overlaps of optical and acoustic field V k q . (b) Dependences of the threshold of the pumping rate of electrons into the conduction band ( W p ¯ / W 0 ) th on the overlap of optical and acoustic field V k q under different dimensionless average phonon injection concentrations n 0 ¯ .
Fig. 4
Fig. 4 (a) Unit cell of the honeycomb-lattice phononic crystal. (b) Irreducible Brillion zone of the honeycomb-lattice phononic crystal.
Fig. 5
Fig. 5 Band structure of the honeycomb-lattice phononic crystal with r/a = 0.25.
Fig. 6
Fig. 6 Schematic of the suspended honeycomb-lattice phononic crystal waveguide structure with a Ge wire defect inside (not to scale).
Fig. 7
Fig. 7 (a)Schematic of honeycomb-lattice phononic crystal waveguide structure. (b) Isometric view and top view for a periodic structural unit of the phononic crystal waveguide.
Fig. 8
Fig. 8 (a) Band structure diagram of the honeycomb-lattice phononic crystal with a wire defect inside. (b)Displacement field distribution corresponding to the blue line. The structural parameters of the supercell are a = 2nm, r/a = 0.25, w = 5nm and h = 3.3nm.
Fig. 9
Fig. 9 Schematic cross-section of waveguide structure.
Fig. 10
Fig. 10 Electric field mode distributions corresponding to different Ge waveguide sizes. (a)400nm × 40nm. (b)80nm × 200nm. (c)400nm × 200nm. (d)600nm × 300nm.
Fig. 11
Fig. 11 Diagrams of the equally distributed displacement field under different structural parameters. (a)20nm × 5nm. (b)25nm × 5nm. (c)30nm × 5nm. (d)20nm × 20nm. (e)20nm × 60nm. (f)Magnified view of the displacement field.
Fig. 12
Fig. 12 Diagrams of the displacement field equally distributed in the z-axis direction under different structural parameters. (a)20nm × 5nm. (b)25nm × 5nm. (c)30nm × 5nm. (d)20nm × 10nm. (e)20nm × 20nm. (f)Magnified view of the displacement field.
Fig. 13
Fig. 13 Normalized acoustic field energy density distribution, as well as the dimensionless phonon concentration along x-axis, where x/w represents the normalized position on x-axis.
Fig. 14
Fig. 14 Overlap of the optical and the acoustic fields V k q as a function of the width of the Ge waveguide w under various heights of the waveguide h.
Fig. 15
Fig. 15 Output characteristics of the photon-phonon laser action under different structural parameters. (a) Dependences of the threshold current Ith on the average injection phonon concentration N 0 ¯ under different waveguide widths and heights. (b) The slope efficiency ΔP/ ΔI as functions of the average injection phonon concentration N 0 ¯ with the waveguide width of 800nm and the height of 400nm. (c) Dependence of the slope efficiency ΔP/ ΔI on the waveguide dimension with N 0 ¯ = 2.5 × 1021 cm−3.

Tables (1)

Tables Icon

Table 1 Material parameters for Ge and notations introduced during the derivation

Equations (48)

Equations on this page are rendered with MathJax. Learn more.

d N e dt = W p W kq W k0 W 0q W 00
d N k dt = 1 τ N k + W kq + W k0 W e
d N q dt = W kq N q τ 0 + N 0 τ 0
W kq =A N k N q [ ( exp μ 0 μ c kT ) 1 ]
A= A t 2 π 2 ( 2 m r 2 ) 3/2 Δ q 0 1/2 =1.9× 10 -10 c m 3 /s
Δ q 0 =h v k +h v q E G
B=3.4× 10 14 c m 3 /s
C=2 A t N c ( 2π ) 3 ( m c 2 ) 3/2 ( m v 2 ) 3/2 Δ q 0 2 =1.3× 10 9 s 1
D= A t N c E G 2 π 2 ( c ) 3 =5.7× 10 -16 c m 3 /s
μ 0 =( h v k +h v q E g ) m v / ( m c + m v )
W k0 =C N k f( μ c / μ 0 )
W 0q =D N q N e
N e = N c 3 π 2 ( 2 m c 2 ) 3/2 μ c 3/2
W 00 =B N e 2
W e =σc N k N e
1 τ = c L ln 1 R
d N e ( x,y,z )dV dt = ( W p ( x,y,z ) W kq ( x,y,z ) W k0 ( x,y,z ) W 00 ( x,y,z ) )dV
d N k ( x,y,z )dV dt = ( N k ( x,y,z )/τ + W kq ( x,y,z ) + W k0 ( x,y,z ) W e ( x,y,z ) )dV
d N q ( x,y,z )dV dt = ( W kq ( x,y,z ) N q ( x,y,z )/ τ 0 + N 0 ( x,y,z )/ τ 0 )dV
AN τ 0 =1
d n e ( x,y,z )dV dθ = W p ( x,y,z ) dV W 0 n k ( x,y,z ) n q ( x,y,z )SdV 0.7×Cτ n k ( x,y,z )dV BτN n e 2 ( x,y,z )dV
d n k ( x,y,z )dV dθ = n k ( x,y,z )dV + n k ( x,y,z ) n q ( x,y,z )SdV +0.7×Cτ n k ( x,y,z ) dVσcτN n k ( x,y,z ) n e ( x,y,z )dV
d n q ( x,y,z )dV dθ = τ τ 0 ( n k ( x,y,z ) n q ( x,y,z )SdV n q ( x,y,z )dV + n 0 ( x,y,z )dV )
n e = N c 3 π 2 N ( 2 m c 2 ) 3/2 μ c 3/2
W p ( x,y,z )dV W 0 = n k ( x,y,z ) n q ( x,y,z )SdV +0.7×Cτ n k ( x,y,z )dV+ BτN n e 2 V
n k ( x,y,z )dV = n k ( x,y,z ) n q ( x,y,z )SdV +0.7×Cτ n k ( x,y,z )dV σcτN n k ( x,y,z ) n e dV
n k ( x,y,z ) n q ( x,y,z )SdV = n q ( x,y,z )dV n 0 ( x,y,z )dV
ΓK= n k ( x,y,z )dV
Γ= Ge Re( E× H * ) z ^ dS total Re( E× H * ) z ^ dS
n k = n k /K
Γ'Q= n q ( x,y,z )dV
n q ' = n q /Q
Γ'Q'= n 0 ( x,y,z )dV
n 0 ' = n 0 / Q'
ΓKQS n k ' ( x,y,z ) n q ' ( x,y,z )dV=QQ'
1 S = ΓKQ n k ' ( x,y,z ) n q ' ( x,y,z )dV QQ' = ΓK V Q V k'q' QQ'
V k q =V n k ' ( x,y,z ) n q ' ( x,y,z )dV
( n e n e0 ) 2 3 =1 kT μ 0 ln( 1 S 1 )
W p ( x,y,z )dV W 0 Γ'Q+Γ'Q'0.7×CτΓKBτN n e 2 V=0
ΓK+Γ'QΓ'Q'+0.7×CτΓKσcτN n e ΓK=0
( n e n e0 ) 2/3 =1 kT μ 0 ln( ΓK V Q V k q Q Q 1 )
W p ¯ / W 0 n q ¯ + n 0 ¯ 0.7×Cτ n k ¯ BτN n e 2 =0
n k ¯ + n q ¯ n 0 ¯ +0.7×Cτ n k ¯ σcτN n e n k ¯ =0
( n e n e0 ) 2/3 =1 kT μ 0 ln( n k ¯ n q ¯ V k q n q ¯ n 0 ¯ 1 )
V k q =V n k ( x,y,z ) n q ( x,y,z )dV = n k ( x,y,z )dV
N 0 ¯ = n 0 ¯ ( N τ 0 /τ )
P= Γhv k c L ln 1 R N k ( x,y,z )dV
I= dQ dt = W p ¯ Ve

Metrics